If θ is an angle in standard position and its terminal side passes through the point (-9,5), find the exact value of sec ⁡ θ secθ in simplest radical form.

Answers

Answer 1

The exact value of secθ secθ in simplest radical form is 106/81.

How to calculate the value

The length of the hypotenuse is the distance from the origin to the point (-9, 5):

√((-9)^2 + 5^2) = √(81 + 25) = √106

cosθ = adjacent/hypotenuse = -9/√106

Therefore, secθ = 1/cosθ = -√106/9.

In order to find the value of secθ secθ, we simply multiply secθ by itself:

secθ secθ = (-√106/9) * (-√106/9) = 106/81

The exact value of secθ secθ is 106/81.

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Related Questions

Ms. Brock runs a house cleaning business. To save money, she bought a 1-gallon container of concentrated cleaner. She mixed the cleaner with 10 gallons of water. Then, she filled as many 1-pint spray bottles as she could. How many spray bottles did she fill?

Answers

Ms. Brock can now fill up to 88 spray bottles with her preparation.

How to find the number of spray bottles she fill

It is calculated that:

one gallon of liquid comprises 128 fluid ounces and one pint has a sum of 16 fluid ounces.

hence we have that

1 gallon = 128 fluid ounces

1 pint = 16 fluid ounces  

cross multiplying

16 fluid ounces x 1 gallon = 128 fluid ounces x 1 pint

1 gallon = (128 fluid ounces x 1 pint) / 16 fluid ounces

1 gallon = 8 pints

Consequently, there are 8 pints in one full gallon.

Ms. Brock blended 1 gallon of cleaner with 10 gallons of water, thus resulting in 11 gallons.

To figure out the total number of pints Ms. Brock has in her solution, we must multiply 11 gallons by 8 pints/gallon:

11 gallons x 8 pints/gallon = 88 pints

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Evaluate the following limits analytically. Show your work for full credit.
Iim (sin(9x))/x
x->0

Answers

The limit of (sin(9x))/x as x approaches 0 is equal to 9.

To evaluate this limit analytically, we can use L'Hopital's Rule.

Taking the derivative of the numerator and denominator with respect to x, we get:lim (sin(9x))/x = lim (9cos(9x))/1as x approaches 0.

Substituting x = 0, we get:lim (sin(9x))/x = 9cos(0)/1 = 9Therefore, the limit of (sin(9x))/x as x approaches 0 is equal to 9.

We know already how to apply or make the procedures mathematically talking so this short program will eventually help you how to find logic.

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Which one is it please help thank you.


The students who attend Memorial High School have a wide variety of extra-curricular activities to choose from in the after-school program. Students are 38% likely to join the dance team; 18% likely to participate in the school play; 42% likely to join the yearbook club; and 64% likely to join the marching band. Many students choose to participate in multiple activities. Students have equal probabilities of being freshmen, sophomores, juniors, or seniors. If Event A = sophomore or junior, what is Event A'?

Answers

Event A' has a probability of 50% (25% for freshmen + 25% for seniors).

To determine Event A', we need to first identify what Event A represents. Event A is the probability that a student is a sophomore or junior. Since students have equal probabilities of being freshmen, sophomores, juniors, or seniors, the probability of Event A is 50% (25% for sophomores + 25% for juniors).
Event A' is the complement of Event A, which means it includes the other two grade levels not included in Event A, in this case, freshmen and seniors. Therefore, Event A' is the probability that a student is a freshman or a senior. Since students have equal probabilities of being in each grade level, Event A' also has a probability of 50% (25% for freshmen + 25% for seniors).

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"When a contractor paints a square surface that has a side length of x feet, he needs to know the area of the surface in order to buy the correct amount of paint. Since the contractor always adds 25 square feet to the area, he buys extra paint. Which function can be used to find the totall area in square feet, Ax , that the contractor will use to determine how much paint he needs to buy?

Answers

The function that can be used to find the total area is: (x^2 + 25) sq. ft.

What is a square?

A square is a type of quadrilateral which has an equal length of sides. So then its area can be calculated as;

area of a square = length x length

We have from the question that; a square surface that has a side length of x feet. So that;

area of the square surface = length * length

                                            = x * x

                                            = x^2 square feet

But since the contractor always adds 25 square feet to the area, he buys extra paint, then the function required is:

total area = (x^2 + 25) sq. ft.

The function is (x^2 + 25) sq. ft.

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Answer:

A(x) = x² + 25

----------------------

In order to find the total area, we need to consider both the area of the square surface and the extra paint he always adds.

Find the area of the square surface:

A = x² (since the side length is x feet)

Add the extra 25 square feet of paint:

A(x) = A + 25

Combining these steps, the function is:

A(x) = x² + 25

A mover notes the weights of a table and 4 chairs and records t+4C >_100 on his invoice. What is he communicating?


The choices are,


A. The table and 4 chairs each weigh more than 100 pounds.


B. The table and 4 chairs weigh at most 100 pounds.


C. The table and 4 chairs weigh around 100 pounds, give or take a little.


D. The table and 4 chairs at


least 100 pounds

Answers

The mover is communicating that the weight of the table and 4 chairs combined, represented as t+4C, is greater than or equal to 100 pounds.

The expression t+4C represents the total weight of the table and 4 chairs. The mover's invoice states that this total weight is greater than or equal to 100 pounds, which means that the combined weight of the table and chairs is at least 100 pounds. Therefore, the correct answer is D, "The table and 4 chairs weigh at least 100 pounds."

To solve this mathematically, we can use algebraic inequalities. The inequality t+4C >_ 100 can be rearranged as t >_ 100-4C. This means that the weight of the table t must be greater than or equal to 100 minus four times the weight of a single chair C.

If each chair weighs less than 25 pounds, then the total weight of the table and 4 chairs combined will be at least 100 pounds. So D is correct answer.

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+
ent will
A circle with center (7,3) and radius of 5 is graphed below with a square inscribed in
the circle.
+
Dillon says to write the equation of the tangent line you need the opposite-reciprocal
slope of the slope of the radius and Chelsey says you need to use the same slope as
the radius. Who is correct and why? Write the equation of the tangent line.
Part B: Find the perimeter of BCDE.

Answers

Chelsey is correct.

The equation of the tangent line is y = 8

Perimeter of BCDE is 28.28

How to determine tangent line and perimeter?

Chelsey is correct. The tangent line at a point on a circle is perpendicular to the radius at that point.

Therefore, it has the same slope as the radius at the point of tangency.

To find the equation of the tangent line at point B(7,8), find the slope of the radius at B.

The radius at B passes through the center of the circle (7,3) and B(7,8), so its slope is:

m = (8 - 3) / (7 - 7) = undefined

This is because the radius is a vertical line. The slope of the tangent line at B is the negative reciprocal of the slope of the radius at B, which is 0.

The equation of the tangent line is:

y - 8 = 0(x - 7)

y = 8

Part B: To find the perimeter of BCDE, we need to find the length of one of its sides and then multiply by 4. Since the square is inscribed in the circle, its diagonal is equal to the diameter of the circle, which is 10 (twice the radius).

Therefore, the length of one side of the square is:

s = 10/√(2) ≈ 7.07

The perimeter of BCDE is:

4s = 4(7.07) ≈ 28.28

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Q 28 : A new school has built lockers for its students. All the digits from 0 to 9, together with


the letters A to Y, have been used to identify the lockers. Only 4 digits have been used to


identify the lockers with the letter Z. How many lockers have been built in this school, if each


locker is identified by one letter and one digit?

Answers

If each locker is identified by one letter and one digit, the total number of lockers built in the school is 229.

There are 26 letters in the alphabet (A to Z), and if each locker is identified by one letter and one digit, then there are a total of 26 × 10 = 260 possible locker identifications using the letters A to Y and digits 0 to 9.

Out of these, there are 4 digits used to identify the lockers with the letter Z. So, there are 10 − 1 = 9 digits left to use for the remaining lockers, as we cannot use the digit already used for the lockers with the letter Z.

Similarly, there are 25 letters left to use for the remaining lockers, as we cannot use the letter Z.

Therefore, the number of remaining lockers is 9 × 25 = 225. Adding the 4 lockers with the letter Z, the total number of lockers built in the school is 225 + 4 = 229.

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Area The measurement of the side of a square floor tile is 10 inches, with a possible error of 1/32 inch.
(a) Use differentials to approximate the possible propagated error in computing the area of the square. (b) Approximate the percent error in computing the area of the square.

Answers

The possible propagated error in computing the area of the square is between 19/32 and 21/32 square inches.

How to calculate the error propagation?

(a) Let A be the area of the square tile. The differential of A with respect to the side length x is dA/dx = 2x.

dA ≈ (dA/dx)dx

At the lower end of the possible range for x, we have:

x = 9 31/32 inches

dx = 1/32 inch

dA = (2x)(dx) = (2(9 31/32))(1/32) = 19/32 square inches

At the upper end of the possible range for x, we have:

x = 10 1/32 inches

dx = 1/32 inch

dA = (2x)(dx) = (2(10 1/32))(1/32) = 21/32 square inches

Therefore, the possible propagated error in computing the area of the square is between 19/32 and 21/32 square inches.

(b) The percent error in computing the area of the square is given by:

(percent error) = (error / actual value) x 100

(percent error) = [(21/32 - 100) / 100] x 100% = -79/1600 x 100% ≈ -4.94%.

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A, B, and C are points of tangency in the given Circle, a m equals 6, BK equals 4 in the perimeter of mkn is 34 ​

Answers

The perimeter of triangle MKN is 34 units.

How to find the length of segment KN?

Based on the information provided, we have a circle with three points of tangency: A, B, and C. Let's consider the triangle formed by these points: MKN.

We are given that the length of AM is 6 and the length of BK is 4. We need to find the perimeter of triangle MKN.

To find the perimeter, we need to know the lengths of all three sides. However, the length of side AC is not provided.

Without additional information, we cannot determine the lengths of sides MN and KN or calculate the perimeter of triangle MKN.

Therefore, with the given information, we cannot find the perimeter of triangle MKN or provide a numerical answer

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f (x) = ¹4 - 6. Find the inverse of f(x) and its domain.
O A. f¹(x) =
6 + 4, where x #-6
O B. f¹(x) =
6 +4, where x #4
O c. f¹(x) =
¹6-4, where x 4
OD. f¹(x) = 2¹6-4, where x#-6

Answers

The correct option is the first one, and the domain is the set of real numbers except for x = -6.

How to find the inverse?

The inverse will be a function such that when we take the composition we get the identity, then we can write:

[tex]f(g(x)) = \frac{1}{g(x) - 4} - 6 = x[/tex]

We need to solve that for g(x), we will get:

[tex]\frac{1}{g(x) - 4} - 6 = x\\\\\frac{1}{g(x) - 4} = x +6\\\\g(x) - 4 = \frac{1}{x + 6} \\g(x) = \frac{1}{x + 6} + 4[/tex]

That is the inverse function, and notice that if x = -6 the denominator becomes zero, so that value is not in the domain.

Then the correct option is the first one.

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Rewrite each expression using a single, positive exponent.

Answers

The given expression, 14⁻³ · 14¹², written as a single, positive exponent is 14⁹

Rewriting an expression using a single exponent

From the question, we are to write the given expression using a single, positive exponent

From the given information,

The given expression is

14⁻³ · 14¹²

This means

14⁻³ × 14¹²

To solve this, let us revise some of the laws of indices

mᵃ × mᵇ = mᵃ ⁺ ᵇmᵃ × mᵇ = mᵃ ⁻ ᵇm⁰ = 1

Thus,

The expression

14⁻³ × 14¹²

can be written as

14⁻³ ⁺ ¹²

14⁹

Hence, the expression written as a single exponent is 14⁹

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Solve for x (2-3) 67

Answers

-67x

x(2-3)•67
x(-1)•67
-67x

Henry's candy jar has the following pleces of candy in it:


3 Snickers


1 Reese's


1 Twix


2 Milky Ways


2 Skittles Packs


Henry will randomly choose one piece of candy,


He will then put it back and randomly choose another piece


of candy. What is the probability that he will


choose a Milky Way and then a Snickers?

Answers

The probability of Henry choosing a Milky Way and then a Snickers is 2/27.


1. First, let's find the total number of candy pieces in Henry's candy jar:
3 Snickers + 1 Reese's + 1 Twix + 2 Milky Ways + 2 Skittles Packs = 9 pieces of candy.

2. Next, we'll calculate the probability of choosing a Milky Way on the first pick:
There are 2 Milky Ways and 9 total pieces of candy, so the probability is 2/9.

3. Since Henry puts the candy back, there are still 9 pieces of candy for the second pick. Now, we'll calculate the probability of choosing a Snickers on the second pick:
There are 3 Snickers and 9 total pieces of candy, so the probability is 3/9 (or 1/3).

4. Finally, we'll multiply the probabilities of each individual event to find the probability of both events occurring together (choosing a Milky Way and then a Snickers):
(2/9) * (1/3) = 2/27

So, the probability of Henry choosing a Milky Way and then a Snickers is 2/27.

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What are two different ways you can solve 2(x – 3) = 8?

Answers

Answer:

There are three methods used to solve systems of equations: graphing, substitution, and elimination.

Step-by-step explanation:

Among american adults, 42. 5 percent are considered: multiple choice question. Obese. Athletic. Anorexic. Underweight

Answers

Answer:

Obese

Step by Step Explanation:

looked it up :)

A pathway made of slate tiles measures​ 5 1/3 ​yards long. A tile measuring ​2​ feet is added to the end of the pathway.

What is the total length of the pathway now?

1. 5 1/3 ft

2. 10 2/3 ft

3. 18 ft

4. 22 ft

Answers

Answer:

18 feet

Step-by-step explanation:

multiply 5 1/3 yards by 3 to find the measurement in feet.

16/3 x 3 = 16

16 + 2 = 18

Helping in the name of Jesus.

the answer to this question is (c)18 feet

The length of a rectangle is 4 m more than the width. if the area of the rectangle is 77 m2. how many meters long is the width of the rectangle?






answer choices d: -11 m: 7 z: 9

Answers

The width of the rectangle is approximately 5.39 meters.

Let's denote the width of the rectangle by x. According to the problem, the length of the rectangle is 4 meters more than the width, which means that the length can be represented as x+4.

The formula for the area of a rectangle is A = length x width. In this case, we know that the area of the rectangle is 77 square meters, so we can set up the following equation:

77 = (x+4)x

Expanding the brackets, we get:

77 = x² + 4x

Rearranging this equation into standard quadratic form, we get:

x² + 4x - 77 = 0

To solve for x, we can use the quadratic formula:

[tex]x = \frac{(-b ± sqrt(b^2 - 4ac))}{ 2a}[/tex]

Plugging in the values for a, b, and c, we get:

[tex]x = \frac{(-4 ± sqrt(4^2 - 4(1)(-77)))}{ 2(1)}[/tex]

Simplifying this expression, we get:

[tex]x = \frac{(-4 ± sqrt(336)} { 2}[/tex]

[tex]x = \frac{(-4 ± 4sqrt(21))}{ 2}[/tex]

x = -2 ± 2[tex]\sqrt{(21)}[/tex]

Since the width of a rectangle cannot be negative, we discard the negative solution and get:

x = -2 ± 2[tex]\sqrt{(21)}[/tex]

Therefore, the width of the rectangle is approximately 5.39 meters (rounded to two decimal places).

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You must build a ramp with a rise of 15 inches to roll some gym equipment into your school. If you follow the ADA specifications:

Answers

To build a ramp with a 15-inch rise for rolling gym equipment into your school, following ADA specifications, we should create a ramp with a run of 180 inches to maintain a 1:12 slope.

For building a ramp with a rise of 15 inches for rolling gym equipment into your school, following ADA specifications. Let's use these terms in our step-by-step explanation:

1. ADA specifications: The Americans with Disabilities Act (ADA) specifies that the slope of a ramp should be no more than 1:12, which means that for every 1 inch of rise, there should be 12 inches of run.

2. Ramp rise: In this case, the rise is 15 inches.

3. Calculate ramp run: To find the ramp run, we can use the ADA specification of 1:12. Multiply the rise (15 inches) by 12.

15 inches x 12 = 180 inches

4. Ramp run: Based on the calculation, the run for the ramp should be 180 inches.

5. Ramp length: To ensure a safe and accessible ramp, follow the ADA specifications and use a ramp length of 180 inches to achieve the 15-inch rise.

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or
Hazel bought 4 souvenirs during 2 days of vacation. How many days will Hazel have to spend on vacation before she will have bought a total of 8 souvenirs? Assume the relationship is directly proportional.

Answers

If Hazel bought 4 in 2 days then in 4 days she will have 8. If you double the amount of souvenirs you will also be doubling the amount of days causing it to be 4.

Fries 420 grams = $2.77
How much if its 1kg?

Answers

420 grams = 2.77
1 gram = 2.77 divided by 420= 0.007 (to 3 decimal places)
1 kilogram= 0.007 x 1000 = $6.60 (2 decimal places)

Answer: $6.60 (i think)

(not too sure, so sorry if i’m wrong!!!!!!)

I NEED HELP ON THIS ASAP!!! IT'S DUE TONIGHT

Answers

Answer:

First Problem:

Transformation: Reflection across the x-axis, shift 2 units rightward

Equation: g(x)=-5^(x-2)

Second Problem:

Transformation: Reflection across the y-axis, shift 4 units upward

Equation: 10^-x+4

Step-by-step explanation:

Imagine folding a piece of paper and using the x or y axis as the crease marks. By folding them and comparing them, we can find out whether it is either the x-axis, y-axis, or both-axis. Then, we move the graph, to match the position in the second picture.

As for equations, exponential functions have the parent function of y=b^(x+c)+h. By plugging in any points given, let's say (1,5), we can see that 5=b^1 and simplifying shows 5=b. Therefore, the function is y=5^x. Using that first equation, we transform it. If over the x-axis, convert y=b^x to y=-b^x. If over the y-axis, convert y=b^x to y=b^-x. For horizontal shift, if going rightward, it is x-c. If going leftward, it is x+c. For vertical shift, if going up, b^x+h. If going down, b^x-h.

If unsure, plug-in points to see if your answer checks out with the equation :)

Find the coordinates of the points on the curve x(????)=3????^2 +1 ????????????y(????)=????^3 −1, for which the tangent linehas a slope of 1/2

Answers

The coordinates of the point on the curve where the tangent line has a slope of 1/2 are (4, 0).

To find the coordinates of the points on the curve x(t) = 3t^2 + 1 and y(t) = t^3 - 1, where the tangent line has a slope of 1/2, follow these steps:

1. Calculate the derivatives of x(t) and y(t) with respect to t:

dx/dt = 6t
dy/dt = 3t^2

2. The slope of the tangent line is given by dy/dx, so calculate dy/dx using the chain rule:

dy/dx = (dy/dt) / (dx/dt) = (3t^2) / (6t) = t/2

3. Set the slope equal to 1/2 and solve for t:

t/2 = 1/2
t = 1

4. Plug the value of t back into the original equations for x(t) and y(t) to find the coordinates of the point:

x(1) = 3(1)^2 + 1 = 4
y(1) = (1)^3 - 1 = 0

The coordinates of the point on the curve where the tangent line has a slope of 1/2 are (4, 0).

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Patricia bought 4 apples and 9 bananas for $12. 70. Jose bought 8 apples and 11 bananas for $17. 70 at the same grocery store. What's the price of one apple?

Answers

the price of one apple after solving the simultaneous equations is $1.45.

Let's denote the price of one apple by "a" and the price of one banana by "b". We can then set up a system of two equations to represent the given information:

4a + 9b = 12.70 (equation 1)
8a + 11b = 17.70 (equation 2)

To solve for the price of one apple, we want to isolate "a" in one of the equations. One way to do this is to multiply equation 1 by 8 and equation 2 by -4, which will allow us to eliminate "b" when we add the two equations together:

(8)(4a + 9b) = (8)(12.70) --> 32a + 72b = 101.60 (equation 3)
(-4)(8a + 11b) = (-4)(17.70) --> -32a - 44b = -70.80 (equation 4)

Adding equations 3 and 4 gives:

28b = 30.80

Solving for "b" yields:

b = 1.10

Substituting this value of "b" into equation 1 gives:

4a + 9(1.10) = 12.70

Solving for "a" yields:

a = 1.45

Therefore, the price of one apple is $1.45.

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Graph the image of △WXY after the following sequence of transformations: Reflection across the y-axis Rotation 180° counterclockwise around the origin

Answers

The old coordinates are;

W (3, 14)

Y (12, 14)

X (6, 11)

While the new coordinates for the reflected triangle are:

W'' (3, -14)

X'' (6, -11)

Y'' (12, -14).

See the attached image.

What is reflection?

A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. The line of reflection is formed when an image reflects through a line.

A figure is said to mirror another figure when every point in one figure is equidistant from every point in another figure.

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Question: P7.18. Convert the following numbers to decimal form: a. * FA 5.6 16; b. * 725.38; c. 3F 4.8 16; d. 73.25 8; e. FF.F 0 16. P7.18.

Answers

a. FA5.6<sub>16</sub> = 15x16<sup>2</sup> + 10x16 + 5 + 6/16 = 4005.375<sub>10</sub>

b. 725.38<sub>10</sub> remains the same in decimal form

c. 3F4.8<sub>16</sub> = 3x16<sup>2</sup> + 15x16 + 4 + 8/16 = 1012.5<sub>10</sub>

d. 73.25<sub>8</sub> = 7x8 + 3 + 2/8 = 59.3125<sub>10</sub>

e. FF.F0<sub>16</sub> = 15x16 + 15 + 15/16 + 0/256 = 255.9375<sub>10</sub>

Decimal form is a way of representing numbers using the base 10 number system. In this system, there are 10 digits from 0 to 9 that are used to represent all possible numbers. Each digit in a decimal number has a place value that is determined by its position. The rightmost digit represents units, the next digit to the left represents tens, and so on, with each successive digit representing higher powers of 10.

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The temperature on skylar’s thermometer last night was −3°f. this morning it was colder. what could be the temperature on her thermometer this morning?−5°f−1°f0°f2°f

Answers

The only option left is −5°F, which is colder than −3°F and thus could be the temperature on her thermometer this morning.

The temperature on Skylar's thermometer is measured using a scale that indicates the degree of hotness or coldness of the atmosphere. In this case, we know that the temperature on her thermometer last night was −3°F. The negative sign indicates that the temperature was below the freezing point of water.

We are asked to determine what the temperature could be on her thermometer this morning. Since we are told that the temperature is colder than −3°F, we can eliminate 0°F and 2°F as possible options, as they are warmer than −3°F.

Similarly, −1°F is only slightly colder than −3°F, so it is unlikely to be the temperature on Skylar's thermometer this morning. Therefore, the only option left is −5°F, which is colder than −3°F and thus could be the temperature on her thermometer this morning.

It is important to note that temperature can have a significant impact on our daily lives. Extreme cold temperatures can cause frostbite, hypothermia, and other health hazards, while hot temperatures can lead to dehydration, heat exhaustion, and heat stroke. It is important to dress appropriately and take necessary precautions when the temperature is too low or too high.

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at a local farmers market a farmer pays $10 to rent a stall and $7 for every hour he stays there. if he pays $45 on saturday how many hours did he stay at the market

Answers

Answer: 5

Step-by-step explanation:

10 + 7h = 45

-10         -10

     7h = 35

divide by 7 to both sides

        h = 5


Solve for x. Round to the nearest hundredth if necessary.
X
24°
14

Answers

Step-by-step explanation:

there is no explanation about x so wierd

1. What is the volume of the sphere?
4

Answers

The volume of the given sphere having radius of 4 units is 267.94 units³.

Given the radius of the sphere (r) = 4 units

To find the volume of the given sphere, we have to substitute the radius in the below volume formula of the sphere,

the volume of the sphere = 4/3 * π * r³

the volume of the given sphere = 4/3 * 3.14 * (4)³        

[π  is approximately equal to 3.14]

the volume of the given sphere = 267.94 units³

So from the above analysis, we can conclude that the volume of the sphere having 4 units radius is 267.94 units³.

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Given question is not having complete information, the complete question is written below:

What is the volume of the sphere having 4 units radius?

A bag has 6 red marbles, 3 blue marbles, and 1 orange marble. In a game to raise money for a class trip, parents pay $5 and pull a marble randomly from the bag. The payout is $10 for pulling an orange marble, $4 for a blue marble, and $1 for a red marble. How much can the class expect to earn per game?

Answers

There are 6 red marbles.
There are 3 blue marbles.
There is 1 orange marble.

To pull a marble from the bag you have to pay $5.

Payout for an orange marble is $10.
Payout for a blue marble is $4.
Payout for a red marble is $1.


Total amount of marbles= 6+3+1
=10.

Multiply the amount of marbles by the amount required to pull a marble
$5^10=$50


Multiply the amount of marbles for each color by the payout.

Red Marbles: 6^1=6
Blue Marbles: 3^4=12
Orange Marbles: 1^10=10

Add the total
$6+$12+$10=$28

Subtract from the $28 from the $50
28-50=22

Therefore, the class can expect to earn approximately $22 per game

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